(k-5)(k-4)=0

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Solution for (k-5)(k-4)=0 equation:


Simplifying
(k + -5)(k + -4) = 0

Reorder the terms:
(-5 + k)(k + -4) = 0

Reorder the terms:
(-5 + k)(-4 + k) = 0

Multiply (-5 + k) * (-4 + k)
(-5(-4 + k) + k(-4 + k)) = 0
((-4 * -5 + k * -5) + k(-4 + k)) = 0
((20 + -5k) + k(-4 + k)) = 0
(20 + -5k + (-4 * k + k * k)) = 0
(20 + -5k + (-4k + k2)) = 0

Combine like terms: -5k + -4k = -9k
(20 + -9k + k2) = 0

Solving
20 + -9k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(4 + -1k)(5 + -1k) = 0

Subproblem 1

Set the factor '(4 + -1k)' equal to zero and attempt to solve: Simplifying 4 + -1k = 0 Solving 4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1k = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1k = 0 + -4 -1k = 0 + -4 Combine like terms: 0 + -4 = -4 -1k = -4 Divide each side by '-1'. k = 4 Simplifying k = 4

Subproblem 2

Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5

Solution

k = {4, 5}

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